The invention relates to characteristic distribution of memory cells in a memory array and, in particular, to a method for evaluating threshold voltage distribution in a memory array by charge pumping.
In a non-volatile memory, threshold voltage distribution is a key concern for memory performance and reliability. Operation of a memory array is impacted by tail bits (cells with minimum Vth) and head bits (cells with maximum Vth) during cell program and erase operations. Thus, it is very important to use an appropriate method to obtain accurate threshold voltage distribution.
FIG. 1 is a conventional test structure for evaluating threshold voltage distribution in a flash memory. The test structure was disclosed in International Conference on Microelectronic Test Structure by Kenji Hakozaki in March, 1973. The test structure 100 comprises a plurality of memory cells 102 connected in parallel. All sources and drains are commonly connected to a voltage Vs and Vd, respectively, while all gates are commonly connected to a voltage Vcg. When a memory cell 102 is operated in a sub-threshold region, a current thereof is expressed as Id=α·10(Vcg−Vth)/S, wherein Vth is threshold voltage. Accordingly, the current increases exponentially with voltage. A slight Vth difference results in a few decades difference of the current and most of the sub-threshold current is derived from only a few bits which have lower Vth. Thus, the minimum threshold voltage can be derived from sub-threshold characteristics.
Conversely, when a memory cell is operated in a linear region, the current is expressed as Id=gm(Vcg−Vth−Vd/2)Vd. The total current of all cells is equal to the product of the mean current by the number of the cells when Vcg is higher than the highest threshold voltage Vth of the measured cells. Thus, the threshold voltage Vth which is estimated from the total Id of all cells is equal to the mean threshold voltage of all cells. In general, the mean threshold voltage is equal to the median threshold voltage of the distribution when the ratio of the tail bits is small.
The conventional method only provides the minimum Vth and/or median Vth of an array from the I-V characteristics. The maximum Vth, however, cannot be extracted from the conventional method. Threshold voltage distribution also cannot be obtained.